LMFDB - Embedded newform 3750.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.71684000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 $ x^8 - 2x^7 - 18x^6 + 10x^5 + 101x^4 + 40x^3 - 132x^2 - 96*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.75978$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.80694 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.80694 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.882586 q^{11} +1.00000 q^{12} -2.82520 q^{13} -4.80694 q^{14} +1.00000 q^{16} +1.65780 q^{17} +1.00000 q^{18} +5.37889 q^{19} -4.80694 q^{21} -0.882586 q^{22} +5.85344 q^{23} +1.00000 q^{24} -2.82520 q^{26} +1.00000 q^{27} -4.80694 q^{28} +3.57827 q^{29} +10.4422 q^{31} +1.00000 q^{32} -0.882586 q^{33} +1.65780 q^{34} +1.00000 q^{36} -1.74607 q^{37} +5.37889 q^{38} -2.82520 q^{39} -1.73520 q^{41} -4.80694 q^{42} +2.27151 q^{43} -0.882586 q^{44} +5.85344 q^{46} -8.72447 q^{47} +1.00000 q^{48} +16.1067 q^{49} +1.65780 q^{51} -2.82520 q^{52} +3.54936 q^{53} +1.00000 q^{54} -4.80694 q^{56} +5.37889 q^{57} +3.57827 q^{58} +10.3536 q^{59} -0.0862540 q^{61} +10.4422 q^{62} -4.80694 q^{63} +1.00000 q^{64} -0.882586 q^{66} +11.9605 q^{67} +1.65780 q^{68} +5.85344 q^{69} -3.50758 q^{71} +1.00000 q^{72} +7.22800 q^{73} -1.74607 q^{74} +5.37889 q^{76} +4.24254 q^{77} -2.82520 q^{78} -12.5762 q^{79} +1.00000 q^{81} -1.73520 q^{82} -13.2741 q^{83} -4.80694 q^{84} +2.27151 q^{86} +3.57827 q^{87} -0.882586 q^{88} +18.6866 q^{89} +13.5806 q^{91} +5.85344 q^{92} +10.4422 q^{93} -8.72447 q^{94} +1.00000 q^{96} +18.2706 q^{97} +16.1067 q^{98} -0.882586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{13} + 4 q^{14} + 8 q^{16} + 14 q^{17} + 8 q^{18} + 10 q^{19} + 4 q^{21} + 6 q^{22} + 12 q^{23} + 8 q^{24} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 10 q^{29} + 16 q^{31} + 8 q^{32} + 6 q^{33} + 14 q^{34} + 8 q^{36} - 6 q^{37} + 10 q^{38} + 2 q^{39} + 6 q^{41} + 4 q^{42} + 2 q^{43} + 6 q^{44} + 12 q^{46} + 14 q^{47} + 8 q^{48} + 26 q^{49} + 14 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{54} + 4 q^{56} + 10 q^{57} + 10 q^{58} + 16 q^{61} + 16 q^{62} + 4 q^{63} + 8 q^{64} + 6 q^{66} - 6 q^{67} + 14 q^{68} + 12 q^{69} + 6 q^{71} + 8 q^{72} - 8 q^{73} - 6 q^{74} + 10 q^{76} + 8 q^{77} + 2 q^{78} + 10 q^{79} + 8 q^{81} + 6 q^{82} + 22 q^{83} + 4 q^{84} + 2 q^{86} + 10 q^{87} + 6 q^{88} + 20 q^{89} + 6 q^{91} + 12 q^{92} + 16 q^{93} + 14 q^{94} + 8 q^{96} - 16 q^{97} + 26 q^{98} + 6 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^13 + 4 * q^14 + 8 * q^16 + 14 * q^17 + 8 * q^18 + 10 * q^19 + 4 * q^21 + 6 * q^22 + 12 * q^23 + 8 * q^24 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 10 * q^29 + 16 * q^31 + 8 * q^32 + 6 * q^33 + 14 * q^34 + 8 * q^36 - 6 * q^37 + 10 * q^38 + 2 * q^39 + 6 * q^41 + 4 * q^42 + 2 * q^43 + 6 * q^44 + 12 * q^46 + 14 * q^47 + 8 * q^48 + 26 * q^49 + 14 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^54 + 4 * q^56 + 10 * q^57 + 10 * q^58 + 16 * q^61 + 16 * q^62 + 4 * q^63 + 8 * q^64 + 6 * q^66 - 6 * q^67 + 14 * q^68 + 12 * q^69 + 6 * q^71 + 8 * q^72 - 8 * q^73 - 6 * q^74 + 10 * q^76 + 8 * q^77 + 2 * q^78 + 10 * q^79 + 8 * q^81 + 6 * q^82 + 22 * q^83 + 4 * q^84 + 2 * q^86 + 10 * q^87 + 6 * q^88 + 20 * q^89 + 6 * q^91 + 12 * q^92 + 16 * q^93 + 14 * q^94 + 8 * q^96 - 16 * q^97 + 26 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−4.80694	−1.81685	−0.908426	−	0.418045i	$-0.862716\pi$
$7$	−4.80694	−1.81685	−0.908426	+	0.418045i	$0.862716\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.882586	−0.266110	−0.133055	−	0.991109i	$-0.542479\pi$
$11$	−0.882586	−0.266110	−0.133055	+	0.991109i	$0.542479\pi$
$12$	1.00000	0.288675
$13$	−2.82520	−0.783570	−0.391785	−	0.920057i	$-0.628142\pi$
$13$	−2.82520	−0.783570	−0.391785	+	0.920057i	$0.628142\pi$
$14$	−4.80694	−1.28471
$15$	0	0
$16$	1.00000	0.250000
$17$	1.65780	0.402076	0.201038	−	0.979583i	$-0.435568\pi$
$17$	1.65780	0.402076	0.201038	+	0.979583i	$0.435568\pi$
$18$	1.00000	0.235702
$19$	5.37889	1.23400	0.617001	−	0.786963i	$-0.288348\pi$
$19$	5.37889	1.23400	0.617001	+	0.786963i	$0.288348\pi$
$20$	0	0
$21$	−4.80694	−1.04896
$22$	−0.882586	−0.188168
$23$	5.85344	1.22053	0.610263	−	0.792199i	$-0.291064\pi$
$23$	5.85344	1.22053	0.610263	+	0.792199i	$0.291064\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.82520	−0.554067
$27$	1.00000	0.192450
$28$	−4.80694	−0.908426
$29$	3.57827	0.664467	0.332234	−	0.943197i	$-0.392198\pi$
$29$	3.57827	0.664467	0.332234	+	0.943197i	$0.392198\pi$
$30$	0	0
$31$	10.4422	1.87547	0.937734	−	0.347355i	$-0.112920\pi$
$31$	10.4422	1.87547	0.937734	+	0.347355i	$0.112920\pi$
$32$	1.00000	0.176777
$33$	−0.882586	−0.153638
$34$	1.65780	0.284311
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.74607	−0.287052	−0.143526	−	0.989647i	$-0.545844\pi$
$37$	−1.74607	−0.287052	−0.143526	+	0.989647i	$0.545844\pi$
$38$	5.37889	0.872571
$39$	−2.82520	−0.452394
$40$	0	0
$41$	−1.73520	−0.270993	−0.135497	−	0.990778i	$-0.543263\pi$
$41$	−1.73520	−0.270993	−0.135497	+	0.990778i	$0.543263\pi$
$42$	−4.80694	−0.741727
$43$	2.27151	0.346403	0.173201	−	0.984886i	$-0.444589\pi$
$43$	2.27151	0.346403	0.173201	+	0.984886i	$0.444589\pi$
$44$	−0.882586	−0.133055
$45$	0	0
$46$	5.85344	0.863042
$47$	−8.72447	−1.27259	−0.636297	−	0.771444i	$-0.719535\pi$
$47$	−8.72447	−1.27259	−0.636297	+	0.771444i	$0.719535\pi$
$48$	1.00000	0.144338
$49$	16.1067	2.30095
$50$	0	0
$51$	1.65780	0.232139
$52$	−2.82520	−0.391785
$53$	3.54936	0.487543	0.243771	−	0.969833i	$-0.421615\pi$
$53$	3.54936	0.487543	0.243771	+	0.969833i	$0.421615\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−4.80694	−0.642354
$57$	5.37889	0.712451
$58$	3.57827	0.469849
$59$	10.3536	1.34793	0.673965	−	0.738763i	$-0.264590\pi$
$59$	10.3536	1.34793	0.673965	+	0.738763i	$0.264590\pi$
$60$	0	0
$61$	−0.0862540	−0.0110437	−0.00552185	−	0.999985i	$-0.501758\pi$
$61$	−0.0862540	−0.0110437	−0.00552185	+	0.999985i	$0.501758\pi$
$62$	10.4422	1.32616
$63$	−4.80694	−0.605618
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.882586	−0.108639
$67$	11.9605	1.46121	0.730606	−	0.682799i	$-0.239238\pi$
$67$	11.9605	1.46121	0.730606	+	0.682799i	$0.239238\pi$
$68$	1.65780	0.201038
$69$	5.85344	0.704671
$70$	0	0
$71$	−3.50758	−0.416273	−0.208137	−	0.978100i	$-0.566740\pi$
$71$	−3.50758	−0.416273	−0.208137	+	0.978100i	$0.566740\pi$
$72$	1.00000	0.117851
$73$	7.22800	0.845973	0.422987	−	0.906136i	$-0.360982\pi$
$73$	7.22800	0.845973	0.422987	+	0.906136i	$0.360982\pi$
$74$	−1.74607	−0.202977
$75$	0	0
$76$	5.37889	0.617001
$77$	4.24254	0.483482
$78$	−2.82520	−0.319891
$79$	−12.5762	−1.41494	−0.707469	−	0.706744i	$-0.750163\pi$
$79$	−12.5762	−1.41494	−0.707469	+	0.706744i	$0.750163\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.73520	−0.191621
$83$	−13.2741	−1.45702	−0.728510	−	0.685036i	$-0.759787\pi$
$83$	−13.2741	−1.45702	−0.728510	+	0.685036i	$0.759787\pi$
$84$	−4.80694	−0.524480
$85$	0	0
$86$	2.27151	0.244944
$87$	3.57827	0.383630
$88$	−0.882586	−0.0940839
$89$	18.6866	1.98078	0.990388	−	0.138318i	$-0.0441697\pi$
$89$	18.6866	1.98078	0.990388	+	0.138318i	$0.0441697\pi$
$90$	0	0
$91$	13.5806	1.42363
$92$	5.85344	0.610263
$93$	10.4422	1.08280
$94$	−8.72447	−0.899860
$95$	0	0
$96$	1.00000	0.102062
$97$	18.2706	1.85510	0.927549	−	0.373701i	$-0.121911\pi$
$97$	18.2706	1.85510	0.927549	+	0.373701i	$0.121911\pi$
$98$	16.1067	1.62702
$99$	−0.882586	−0.0887032
$100$	0	0
$101$	−5.46110	−0.543400	−0.271700	−	0.962382i	$-0.587586\pi$
$101$	−5.46110	−0.543400	−0.271700	+	0.962382i	$0.587586\pi$
$102$	1.65780	0.164147
$103$	−6.64235	−0.654490	−0.327245	−	0.944940i	$-0.606120\pi$
$103$	−6.64235	−0.654490	−0.327245	+	0.944940i	$0.606120\pi$
$104$	−2.82520	−0.277034
$105$	0	0
$106$	3.54936	0.344745
$107$	14.5245	1.40414	0.702070	−	0.712108i	$-0.252259\pi$
$107$	14.5245	1.40414	0.702070	+	0.712108i	$0.252259\pi$
$108$	1.00000	0.0962250
$109$	4.77065	0.456945	0.228473	−	0.973550i	$-0.426627\pi$
$109$	4.77065	0.456945	0.228473	+	0.973550i	$0.426627\pi$
$110$	0	0
$111$	−1.74607	−0.165730
$112$	−4.80694	−0.454213
$113$	−4.83558	−0.454893	−0.227446	−	0.973791i	$-0.573038\pi$
$113$	−4.83558	−0.454893	−0.227446	+	0.973791i	$0.573038\pi$
$114$	5.37889	0.503779
$115$	0	0
$116$	3.57827	0.332234
$117$	−2.82520	−0.261190
$118$	10.3536	0.953131
$119$	−7.96896	−0.730513
$120$	0	0
$121$	−10.2210	−0.929186
$122$	−0.0862540	−0.00780907
$123$	−1.73520	−0.156458
$124$	10.4422	0.937734
$125$	0	0
$126$	−4.80694	−0.428236
$127$	−1.80181	−0.159885	−0.0799423	−	0.996799i	$-0.525474\pi$
$127$	−1.80181	−0.159885	−0.0799423	+	0.996799i	$0.525474\pi$
$128$	1.00000	0.0883883
$129$	2.27151	0.199996
$130$	0	0
$131$	−16.0315	−1.40068	−0.700338	−	0.713812i	$-0.746967\pi$
$131$	−16.0315	−1.40068	−0.700338	+	0.713812i	$0.746967\pi$
$132$	−0.882586	−0.0768192
$133$	−25.8560	−2.24200
$134$	11.9605	1.03323
$135$	0	0
$136$	1.65780	0.142155
$137$	−1.76718	−0.150981	−0.0754904	−	0.997147i	$-0.524052\pi$
$137$	−1.76718	−0.150981	−0.0754904	+	0.997147i	$0.524052\pi$
$138$	5.85344	0.498278
$139$	10.9965	0.932712	0.466356	−	0.884597i	$-0.345567\pi$
$139$	10.9965	0.932712	0.466356	+	0.884597i	$0.345567\pi$
$140$	0	0
$141$	−8.72447	−0.734733
$142$	−3.50758	−0.294350
$143$	2.49348	0.208515
$144$	1.00000	0.0833333
$145$	0	0
$146$	7.22800	0.598194
$147$	16.1067	1.32846
$148$	−1.74607	−0.143526
$149$	2.90948	0.238354	0.119177	−	0.992873i	$-0.461974\pi$
$149$	2.90948	0.238354	0.119177	+	0.992873i	$0.461974\pi$
$150$	0	0
$151$	−1.34184	−0.109197	−0.0545986	−	0.998508i	$-0.517388\pi$
$151$	−1.34184	−0.109197	−0.0545986	+	0.998508i	$0.517388\pi$
$152$	5.37889	0.436285
$153$	1.65780	0.134025
$154$	4.24254	0.341873
$155$	0	0
$156$	−2.82520	−0.226197
$157$	−8.31169	−0.663345	−0.331673	−	0.943395i	$-0.607613\pi$
$157$	−8.31169	−0.663345	−0.331673	+	0.943395i	$0.607613\pi$
$158$	−12.5762	−1.00051
$159$	3.54936	0.281483
$160$	0	0
$161$	−28.1371	−2.21752
$162$	1.00000	0.0785674
$163$	−6.23874	−0.488656	−0.244328	−	0.969693i	$-0.578567\pi$
$163$	−6.23874	−0.488656	−0.244328	+	0.969693i	$0.578567\pi$
$164$	−1.73520	−0.135497
$165$	0	0
$166$	−13.2741	−1.03027
$167$	14.8368	1.14811	0.574054	−	0.818818i	$-0.305370\pi$
$167$	14.8368	1.14811	0.574054	+	0.818818i	$0.305370\pi$
$168$	−4.80694	−0.370864
$169$	−5.01824	−0.386019
$170$	0	0
$171$	5.37889	0.411334
$172$	2.27151	0.173201
$173$	−16.0369	−1.21926	−0.609630	−	0.792686i	$-0.708682\pi$
$173$	−16.0369	−1.21926	−0.609630	+	0.792686i	$0.708682\pi$
$174$	3.57827	0.271268
$175$	0	0
$176$	−0.882586	−0.0665274
$177$	10.3536	0.778228
$178$	18.6866	1.40062
$179$	11.7489	0.878154	0.439077	−	0.898449i	$-0.355306\pi$
$179$	11.7489	0.878154	0.439077	+	0.898449i	$0.355306\pi$
$180$	0	0
$181$	−4.03402	−0.299846	−0.149923	−	0.988698i	$-0.547903\pi$
$181$	−4.03402	−0.299846	−0.149923	+	0.988698i	$0.547903\pi$
$182$	13.5806	1.00666
$183$	−0.0862540	−0.00637608
$184$	5.85344	0.431521
$185$	0	0
$186$	10.4422	0.765656
$187$	−1.46315	−0.106996
$188$	−8.72447	−0.636297
$189$	−4.80694	−0.349653
$190$	0	0
$191$	11.9215	0.862611	0.431306	−	0.902206i	$-0.358053\pi$
$191$	11.9215	0.862611	0.431306	+	0.902206i	$0.358053\pi$
$192$	1.00000	0.0721688
$193$	11.8088	0.850019	0.425009	−	0.905189i	$-0.360271\pi$
$193$	11.8088	0.850019	0.425009	+	0.905189i	$0.360271\pi$
$194$	18.2706	1.31175
$195$	0	0
$196$	16.1067	1.15048
$197$	−7.27842	−0.518566	−0.259283	−	0.965801i	$-0.583486\pi$
$197$	−7.27842	−0.518566	−0.259283	+	0.965801i	$0.583486\pi$
$198$	−0.882586	−0.0627226
$199$	2.27949	0.161589	0.0807944	−	0.996731i	$-0.474254\pi$
$199$	2.27949	0.161589	0.0807944	+	0.996731i	$0.474254\pi$
$200$	0	0
$201$	11.9605	0.843631
$202$	−5.46110	−0.384242
$203$	−17.2005	−1.20724
$204$	1.65780	0.116069
$205$	0	0
$206$	−6.64235	−0.462794
$207$	5.85344	0.406842
$208$	−2.82520	−0.195892
$209$	−4.74733	−0.328380
$210$	0	0
$211$	−1.24920	−0.0859983	−0.0429991	−	0.999075i	$-0.513691\pi$
$211$	−1.24920	−0.0859983	−0.0429991	+	0.999075i	$0.513691\pi$
$212$	3.54936	0.243771
$213$	−3.50758	−0.240336
$214$	14.5245	0.992877
$215$	0	0
$216$	1.00000	0.0680414
$217$	−50.1948	−3.40745
$218$	4.77065	0.323109
$219$	7.22800	0.488423
$220$	0	0
$221$	−4.68363	−0.315055
$222$	−1.74607	−0.117189
$223$	8.84212	0.592112	0.296056	−	0.955171i	$-0.404328\pi$
$223$	8.84212	0.592112	0.296056	+	0.955171i	$0.404328\pi$
$224$	−4.80694	−0.321177
$225$	0	0
$226$	−4.83558	−0.321658
$227$	−17.6968	−1.17457	−0.587287	−	0.809379i	$-0.699804\pi$
$227$	−17.6968	−1.17457	−0.587287	+	0.809379i	$0.699804\pi$
$228$	5.37889	0.356226
$229$	−8.91363	−0.589029	−0.294515	−	0.955647i	$-0.595158\pi$
$229$	−8.91363	−0.589029	−0.294515	+	0.955647i	$0.595158\pi$
$230$	0	0
$231$	4.24254	0.279138
$232$	3.57827	0.234925
$233$	−9.59063	−0.628303	−0.314151	−	0.949373i	$-0.601720\pi$
$233$	−9.59063	−0.628303	−0.314151	+	0.949373i	$0.601720\pi$
$234$	−2.82520	−0.184689
$235$	0	0
$236$	10.3536	0.673965
$237$	−12.5762	−0.816915
$238$	−7.96896	−0.516551
$239$	−9.16299	−0.592704	−0.296352	−	0.955079i	$-0.595770\pi$
$239$	−9.16299	−0.592704	−0.296352	+	0.955079i	$0.595770\pi$
$240$	0	0
$241$	−2.49551	−0.160750	−0.0803749	−	0.996765i	$-0.525612\pi$
$241$	−2.49551	−0.160750	−0.0803749	+	0.996765i	$0.525612\pi$
$242$	−10.2210	−0.657034
$243$	1.00000	0.0641500
$244$	−0.0862540	−0.00552185
$245$	0	0
$246$	−1.73520	−0.110632
$247$	−15.1964	−0.966926
$248$	10.4422	0.663078
$249$	−13.2741	−0.841211
$250$	0	0
$251$	8.71262	0.549936	0.274968	−	0.961453i	$-0.411333\pi$
$251$	8.71262	0.549936	0.274968	+	0.961453i	$0.411333\pi$
$252$	−4.80694	−0.302809
$253$	−5.16616	−0.324794
$254$	−1.80181	−0.113056
$255$	0	0
$256$	1.00000	0.0625000
$257$	−19.7871	−1.23429	−0.617143	−	0.786851i	$-0.711710\pi$
$257$	−19.7871	−1.23429	−0.617143	+	0.786851i	$0.711710\pi$
$258$	2.27151	0.141418
$259$	8.39326	0.521532
$260$	0	0
$261$	3.57827	0.221489
$262$	−16.0315	−0.990427
$263$	25.5635	1.57631	0.788155	−	0.615477i	$-0.211036\pi$
$263$	25.5635	1.57631	0.788155	+	0.615477i	$0.211036\pi$
$264$	−0.882586	−0.0543194
$265$	0	0
$266$	−25.8560	−1.58533
$267$	18.6866	1.14360
$268$	11.9605	0.730606
$269$	24.4144	1.48857	0.744286	−	0.667861i	$-0.232790\pi$
$269$	24.4144	1.48857	0.744286	+	0.667861i	$0.232790\pi$
$270$	0	0
$271$	2.74652	0.166839	0.0834195	−	0.996515i	$-0.473416\pi$
$271$	2.74652	0.166839	0.0834195	+	0.996515i	$0.473416\pi$
$272$	1.65780	0.100519
$273$	13.5806	0.821934
$274$	−1.76718	−0.106760
$275$	0	0
$276$	5.85344	0.352336
$277$	2.98079	0.179098	0.0895490	−	0.995982i	$-0.471457\pi$
$277$	2.98079	0.179098	0.0895490	+	0.995982i	$0.471457\pi$
$278$	10.9965	0.659527
$279$	10.4422	0.625156
$280$	0	0
$281$	3.86174	0.230372	0.115186	−	0.993344i	$-0.463254\pi$
$281$	3.86174	0.230372	0.115186	+	0.993344i	$0.463254\pi$
$282$	−8.72447	−0.519534
$283$	−16.7019	−0.992825	−0.496412	−	0.868087i	$-0.665350\pi$
$283$	−16.7019	−0.992825	−0.496412	+	0.868087i	$0.665350\pi$
$284$	−3.50758	−0.208137
$285$	0	0
$286$	2.49348	0.147443
$287$	8.34102	0.492355
$288$	1.00000	0.0589256
$289$	−14.2517	−0.838335
$290$	0	0
$291$	18.2706	1.07104
$292$	7.22800	0.422987
$293$	−0.503153	−0.0293945	−0.0146972	−	0.999892i	$-0.504678\pi$
$293$	−0.503153	−0.0293945	−0.0146972	+	0.999892i	$0.504678\pi$
$294$	16.1067	0.939361
$295$	0	0
$296$	−1.74607	−0.101488
$297$	−0.882586	−0.0512128
$298$	2.90948	0.168542
$299$	−16.5371	−0.956367
$300$	0	0
$301$	−10.9190	−0.629363
$302$	−1.34184	−0.0772141
$303$	−5.46110	−0.313732
$304$	5.37889	0.308500
$305$	0	0
$306$	1.65780	0.0947703
$307$	−8.63375	−0.492754	−0.246377	−	0.969174i	$-0.579240\pi$
$307$	−8.63375	−0.492754	−0.246377	+	0.969174i	$0.579240\pi$
$308$	4.24254	0.241741
$309$	−6.64235	−0.377870
$310$	0	0
$311$	20.2674	1.14926	0.574630	−	0.818413i	$-0.305146\pi$
$311$	20.2674	1.14926	0.574630	+	0.818413i	$0.305146\pi$
$312$	−2.82520	−0.159945
$313$	−17.0302	−0.962604	−0.481302	−	0.876555i	$-0.659836\pi$
$313$	−17.0302	−0.962604	−0.481302	+	0.876555i	$0.659836\pi$
$314$	−8.31169	−0.469056
$315$	0	0
$316$	−12.5762	−0.707469
$317$	−2.82157	−0.158475	−0.0792375	−	0.996856i	$-0.525249\pi$
$317$	−2.82157	−0.158475	−0.0792375	+	0.996856i	$0.525249\pi$
$318$	3.54936	0.199038
$319$	−3.15813	−0.176821
$320$	0	0
$321$	14.5245	0.810681
$322$	−28.1371	−1.56802
$323$	8.91713	0.496163
$324$	1.00000	0.0555556
$325$	0	0
$326$	−6.23874	−0.345532
$327$	4.77065	0.263817
$328$	−1.73520	−0.0958105
$329$	41.9380	2.31212
$330$	0	0
$331$	−4.07299	−0.223872	−0.111936	−	0.993715i	$-0.535705\pi$
$331$	−4.07299	−0.223872	−0.111936	+	0.993715i	$0.535705\pi$
$332$	−13.2741	−0.728510
$333$	−1.74607	−0.0956840
$334$	14.8368	0.811835
$335$	0	0
$336$	−4.80694	−0.262240
$337$	−9.04782	−0.492866	−0.246433	−	0.969160i	$-0.579259\pi$
$337$	−9.04782	−0.492866	−0.246433	+	0.969160i	$0.579259\pi$
$338$	−5.01824	−0.272956
$339$	−4.83558	−0.262632
$340$	0	0
$341$	−9.21610	−0.499080
$342$	5.37889	0.290857
$343$	−43.7753	−2.36364
$344$	2.27151	0.122472
$345$	0	0
$346$	−16.0369	−0.862147
$347$	8.68656	0.466319	0.233159	−	0.972439i	$-0.425094\pi$
$347$	8.68656	0.466319	0.233159	+	0.972439i	$0.425094\pi$
$348$	3.57827	0.191815
$349$	26.8305	1.43620	0.718101	−	0.695938i	$-0.245011\pi$
$349$	26.8305	1.43620	0.718101	+	0.695938i	$0.245011\pi$
$350$	0	0
$351$	−2.82520	−0.150798
$352$	−0.882586	−0.0470420
$353$	−28.3499	−1.50891	−0.754456	−	0.656351i	$-0.772099\pi$
$353$	−28.3499	−1.50891	−0.754456	+	0.656351i	$0.772099\pi$
$354$	10.3536	0.550290
$355$	0	0
$356$	18.6866	0.990388
$357$	−7.96896	−0.421762
$358$	11.7489	0.620949
$359$	8.68830	0.458551	0.229276	−	0.973362i	$-0.426364\pi$
$359$	8.68830	0.458551	0.229276	+	0.973362i	$0.426364\pi$
$360$	0	0
$361$	9.93243	0.522760
$362$	−4.03402	−0.212023
$363$	−10.2210	−0.536466
$364$	13.5806	0.711815
$365$	0	0
$366$	−0.0862540	−0.00450857
$367$	−12.4713	−0.650998	−0.325499	−	0.945542i	$-0.605532\pi$
$367$	−12.4713	−0.650998	−0.325499	+	0.945542i	$0.605532\pi$
$368$	5.85344	0.305132
$369$	−1.73520	−0.0903310
$370$	0	0
$371$	−17.0616	−0.885793
$372$	10.4422	0.541401
$373$	−12.9988	−0.673050	−0.336525	−	0.941674i	$-0.609252\pi$
$373$	−12.9988	−0.673050	−0.336525	+	0.941674i	$0.609252\pi$
$374$	−1.46315	−0.0756578
$375$	0	0
$376$	−8.72447	−0.449930
$377$	−10.1093	−0.520656
$378$	−4.80694	−0.247242
$379$	1.75227	0.0900080	0.0450040	−	0.998987i	$-0.485670\pi$
$379$	1.75227	0.0900080	0.0450040	+	0.998987i	$0.485670\pi$
$380$	0	0
$381$	−1.80181	−0.0923095
$382$	11.9215	0.609958
$383$	34.1359	1.74426	0.872131	−	0.489272i	$-0.162738\pi$
$383$	34.1359	1.74426	0.872131	+	0.489272i	$0.162738\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	11.8088	0.601054
$387$	2.27151	0.115468
$388$	18.2706	0.927549
$389$	6.85652	0.347640	0.173820	−	0.984777i	$-0.444389\pi$
$389$	6.85652	0.347640	0.173820	+	0.984777i	$0.444389\pi$
$390$	0	0
$391$	9.70385	0.490745
$392$	16.1067	0.813510
$393$	−16.0315	−0.808680
$394$	−7.27842	−0.366682
$395$	0	0
$396$	−0.882586	−0.0443516
$397$	−33.1587	−1.66419	−0.832093	−	0.554636i	$-0.812858\pi$
$397$	−33.1587	−1.66419	−0.832093	+	0.554636i	$0.812858\pi$
$398$	2.27949	0.114261
$399$	−25.8560	−1.29442
$400$	0	0
$401$	3.51432	0.175497	0.0877483	−	0.996143i	$-0.472033\pi$
$401$	3.51432	0.175497	0.0877483	+	0.996143i	$0.472033\pi$
$402$	11.9605	0.596537
$403$	−29.5012	−1.46956
$404$	−5.46110	−0.271700
$405$	0	0
$406$	−17.2005	−0.853647
$407$	1.54106	0.0763873
$408$	1.65780	0.0820735
$409$	−16.2848	−0.805230	−0.402615	−	0.915370i	$-0.631899\pi$
$409$	−16.2848	−0.805230	−0.402615	+	0.915370i	$0.631899\pi$
$410$	0	0
$411$	−1.76718	−0.0871688
$412$	−6.64235	−0.327245
$413$	−49.7694	−2.44899
$414$	5.85344	0.287681
$415$	0	0
$416$	−2.82520	−0.138517
$417$	10.9965	0.538501
$418$	−4.74733	−0.232199
$419$	26.4881	1.29403	0.647015	−	0.762477i	$-0.276017\pi$
$419$	26.4881	1.29403	0.647015	+	0.762477i	$0.276017\pi$
$420$	0	0
$421$	−30.9522	−1.50852	−0.754260	−	0.656576i	$-0.772004\pi$
$421$	−30.9522	−1.50852	−0.754260	+	0.656576i	$0.772004\pi$
$422$	−1.24920	−0.0608100
$423$	−8.72447	−0.424198
$424$	3.54936	0.172372
$425$	0	0
$426$	−3.50758	−0.169943
$427$	0.414618	0.0200648
$428$	14.5245	0.702070
$429$	2.49348	0.120386
$430$	0	0
$431$	−1.72282	−0.0829854	−0.0414927	−	0.999139i	$-0.513211\pi$
$431$	−1.72282	−0.0829854	−0.0414927	+	0.999139i	$0.513211\pi$
$432$	1.00000	0.0481125
$433$	24.1382	1.16001	0.580003	−	0.814614i	$-0.303051\pi$
$433$	24.1382	1.16001	0.580003	+	0.814614i	$0.303051\pi$
$434$	−50.1948	−2.40943
$435$	0	0
$436$	4.77065	0.228473
$437$	31.4850	1.50613
$438$	7.22800	0.345367
$439$	8.24333	0.393433	0.196716	−	0.980460i	$-0.436972\pi$
$439$	8.24333	0.393433	0.196716	+	0.980460i	$0.436972\pi$
$440$	0	0
$441$	16.1067	0.766985
$442$	−4.68363	−0.222777
$443$	22.4652	1.06735	0.533676	−	0.845689i	$-0.320810\pi$
$443$	22.4652	1.06735	0.533676	+	0.845689i	$0.320810\pi$
$444$	−1.74607	−0.0828648
$445$	0	0
$446$	8.84212	0.418687
$447$	2.90948	0.137614
$448$	−4.80694	−0.227107
$449$	30.4988	1.43933	0.719663	−	0.694323i	$-0.244296\pi$
$449$	30.4988	1.43933	0.719663	+	0.694323i	$0.244296\pi$
$450$	0	0
$451$	1.53146	0.0721139
$452$	−4.83558	−0.227446
$453$	−1.34184	−0.0630451
$454$	−17.6968	−0.830550
$455$	0	0
$456$	5.37889	0.251889
$457$	−6.65272	−0.311201	−0.155601	−	0.987820i	$-0.549731\pi$
$457$	−6.65272	−0.311201	−0.155601	+	0.987820i	$0.549731\pi$
$458$	−8.91363	−0.416507
$459$	1.65780	0.0773796
$460$	0	0
$461$	−23.6681	−1.10233	−0.551167	−	0.834395i	$-0.685817\pi$
$461$	−23.6681	−1.10233	−0.551167	+	0.834395i	$0.685817\pi$
$462$	4.24254	0.197381
$463$	26.0857	1.21230	0.606152	−	0.795348i	$-0.292712\pi$
$463$	26.0857	1.21230	0.606152	+	0.795348i	$0.292712\pi$
$464$	3.57827	0.166117
$465$	0	0
$466$	−9.59063	−0.444277
$467$	−1.47562	−0.0682837	−0.0341419	−	0.999417i	$-0.510870\pi$
$467$	−1.47562	−0.0682837	−0.0341419	+	0.999417i	$0.510870\pi$
$468$	−2.82520	−0.130595
$469$	−57.4936	−2.65481
$470$	0	0
$471$	−8.31169	−0.382983
$472$	10.3536	0.476565
$473$	−2.00481	−0.0921810
$474$	−12.5762	−0.577646
$475$	0	0
$476$	−7.96896	−0.365257
$477$	3.54936	0.162514
$478$	−9.16299	−0.419105
$479$	−13.4099	−0.612713	−0.306357	−	0.951917i	$-0.599110\pi$
$479$	−13.4099	−0.612713	−0.306357	+	0.951917i	$0.599110\pi$
$480$	0	0
$481$	4.93300	0.224925
$482$	−2.49551	−0.113667
$483$	−28.1371	−1.28028
$484$	−10.2210	−0.464593
$485$	0	0
$486$	1.00000	0.0453609
$487$	−2.12008	−0.0960701	−0.0480351	−	0.998846i	$-0.515296\pi$
$487$	−2.12008	−0.0960701	−0.0480351	+	0.998846i	$0.515296\pi$
$488$	−0.0862540	−0.00390454
$489$	−6.23874	−0.282125
$490$	0	0
$491$	−2.22427	−0.100380	−0.0501900	−	0.998740i	$-0.515983\pi$
$491$	−2.22427	−0.100380	−0.0501900	+	0.998740i	$0.515983\pi$
$492$	−1.73520	−0.0782290
$493$	5.93206	0.267166
$494$	−15.1964	−0.683720
$495$	0	0
$496$	10.4422	0.468867
$497$	16.8607	0.756307
$498$	−13.2741	−0.594826
$499$	14.5582	0.651715	0.325858	−	0.945419i	$-0.394347\pi$
$499$	14.5582	0.651715	0.325858	+	0.945419i	$0.394347\pi$
$500$	0	0
$501$	14.8368	0.662860
$502$	8.71262	0.388863
$503$	23.8412	1.06303	0.531514	−	0.847050i	$-0.321623\pi$
$503$	23.8412	1.06303	0.531514	+	0.847050i	$0.321623\pi$
$504$	−4.80694	−0.214118
$505$	0	0
$506$	−5.16616	−0.229664
$507$	−5.01824	−0.222868
$508$	−1.80181	−0.0799423
$509$	−34.8006	−1.54251	−0.771255	−	0.636527i	$-0.780370\pi$
$509$	−34.8006	−1.54251	−0.771255	+	0.636527i	$0.780370\pi$
$510$	0	0
$511$	−34.7446	−1.53701
$512$	1.00000	0.0441942
$513$	5.37889	0.237484
$514$	−19.7871	−0.872772
$515$	0	0
$516$	2.27151	0.0999978
$517$	7.70009	0.338649
$518$	8.39326	0.368778
$519$	−16.0369	−0.703940
$520$	0	0
$521$	−8.69128	−0.380772	−0.190386	−	0.981709i	$-0.560974\pi$
$521$	−8.69128	−0.380772	−0.190386	+	0.981709i	$0.560974\pi$
$522$	3.57827	0.156616
$523$	32.4362	1.41834	0.709168	−	0.705040i	$-0.249071\pi$
$523$	32.4362	1.41834	0.709168	+	0.705040i	$0.249071\pi$
$524$	−16.0315	−0.700338
$525$	0	0
$526$	25.5635	1.11462
$527$	17.3110	0.754081
$528$	−0.882586	−0.0384096
$529$	11.2627	0.489684
$530$	0	0
$531$	10.3536	0.449310
$532$	−25.8560	−1.12100
$533$	4.90230	0.212342
$534$	18.6866	0.808648
$535$	0	0
$536$	11.9605	0.516616
$537$	11.7489	0.507002
$538$	24.4144	1.05258
$539$	−14.2155	−0.612306
$540$	0	0
$541$	30.9017	1.32857	0.664284	−	0.747480i	$-0.268736\pi$
$541$	30.9017	1.32857	0.664284	+	0.747480i	$0.268736\pi$
$542$	2.74652	0.117973
$543$	−4.03402	−0.173116
$544$	1.65780	0.0710777
$545$	0	0
$546$	13.5806	0.581195
$547$	−31.2615	−1.33665	−0.668323	−	0.743871i	$-0.732988\pi$
$547$	−31.2615	−1.33665	−0.668323	+	0.743871i	$0.732988\pi$
$548$	−1.76718	−0.0754904
$549$	−0.0862540	−0.00368123
$550$	0	0
$551$	19.2471	0.819953
$552$	5.85344	0.249139
$553$	60.4533	2.57074
$554$	2.98079	0.126641
$555$	0	0
$556$	10.9965	0.466356
$557$	34.8113	1.47500	0.737500	−	0.675347i	$-0.236006\pi$
$557$	34.8113	1.47500	0.737500	+	0.675347i	$0.236006\pi$
$558$	10.4422	0.442052
$559$	−6.41748	−0.271431
$560$	0	0
$561$	−1.46315	−0.0617744
$562$	3.86174	0.162898
$563$	4.89154	0.206154	0.103077	−	0.994673i	$-0.467131\pi$
$563$	4.89154	0.206154	0.103077	+	0.994673i	$0.467131\pi$
$564$	−8.72447	−0.367366
$565$	0	0
$566$	−16.7019	−0.702033
$567$	−4.80694	−0.201873
$568$	−3.50758	−0.147175
$569$	−2.93505	−0.123044	−0.0615218	−	0.998106i	$-0.519595\pi$
$569$	−2.93505	−0.123044	−0.0615218	+	0.998106i	$0.519595\pi$
$570$	0	0
$571$	31.8853	1.33436	0.667179	−	0.744897i	$-0.267501\pi$
$571$	31.8853	1.33436	0.667179	+	0.744897i	$0.267501\pi$
$572$	2.49348	0.104258
$573$	11.9215	0.498029
$574$	8.34102	0.348147
$575$	0	0
$576$	1.00000	0.0416667
$577$	−36.9614	−1.53872	−0.769362	−	0.638813i	$-0.779426\pi$
$577$	−36.9614	−1.53872	−0.769362	+	0.638813i	$0.779426\pi$
$578$	−14.2517	−0.592792
$579$	11.8088	0.490759
$580$	0	0
$581$	63.8077	2.64719
$582$	18.2706	0.757341
$583$	−3.13262	−0.129740
$584$	7.22800	0.299097
$585$	0	0
$586$	−0.503153	−0.0207850
$587$	28.0605	1.15818	0.579090	−	0.815263i	$-0.303408\pi$
$587$	28.0605	1.15818	0.579090	+	0.815263i	$0.303408\pi$
$588$	16.1067	0.664228
$589$	56.1672	2.31433
$590$	0	0
$591$	−7.27842	−0.299394
$592$	−1.74607	−0.0717630
$593$	−40.6263	−1.66832	−0.834161	−	0.551521i	$-0.814048\pi$
$593$	−40.6263	−1.66832	−0.834161	+	0.551521i	$0.814048\pi$
$594$	−0.882586	−0.0362129
$595$	0	0
$596$	2.90948	0.119177
$597$	2.27949	0.0932933
$598$	−16.5371	−0.676254
$599$	−22.6989	−0.927451	−0.463725	−	0.885979i	$-0.653488\pi$
$599$	−22.6989	−0.927451	−0.463725	+	0.885979i	$0.653488\pi$
$600$	0	0
$601$	32.9640	1.34463	0.672316	−	0.740265i	$-0.265300\pi$
$601$	32.9640	1.34463	0.672316	+	0.740265i	$0.265300\pi$
$602$	−10.9190	−0.445027
$603$	11.9605	0.487071
$604$	−1.34184	−0.0545986
$605$	0	0
$606$	−5.46110	−0.221842
$607$	8.32854	0.338045	0.169023	−	0.985612i	$-0.445939\pi$
$607$	8.32854	0.338045	0.169023	+	0.985612i	$0.445939\pi$
$608$	5.37889	0.218143
$609$	−17.2005	−0.697000
$610$	0	0
$611$	24.6484	0.997166
$612$	1.65780	0.0670127
$613$	−7.37261	−0.297777	−0.148889	−	0.988854i	$-0.547570\pi$
$613$	−7.37261	−0.297777	−0.148889	+	0.988854i	$0.547570\pi$
$614$	−8.63375	−0.348430
$615$	0	0
$616$	4.24254	0.170937
$617$	−8.86603	−0.356933	−0.178466	−	0.983946i	$-0.557114\pi$
$617$	−8.86603	−0.356933	−0.178466	+	0.983946i	$0.557114\pi$
$618$	−6.64235	−0.267194
$619$	−0.451385	−0.0181427	−0.00907134	−	0.999959i	$-0.502888\pi$
$619$	−0.451385	−0.0181427	−0.00907134	+	0.999959i	$0.502888\pi$
$620$	0	0
$621$	5.85344	0.234890
$622$	20.2674	0.812649
$623$	−89.8254	−3.59878
$624$	−2.82520	−0.113099
$625$	0	0
$626$	−17.0302	−0.680664
$627$	−4.74733	−0.189590
$628$	−8.31169	−0.331673
$629$	−2.89464	−0.115417
$630$	0	0
$631$	−31.5501	−1.25599	−0.627995	−	0.778217i	$-0.716124\pi$
$631$	−31.5501	−1.25599	−0.627995	+	0.778217i	$0.716124\pi$
$632$	−12.5762	−0.500256
$633$	−1.24920	−0.0496511
$634$	−2.82157	−0.112059
$635$	0	0
$636$	3.54936	0.140741
$637$	−45.5046	−1.80296
$638$	−3.15813	−0.125031
$639$	−3.50758	−0.138758
$640$	0	0
$641$	18.6782	0.737745	0.368872	−	0.929480i	$-0.379744\pi$
$641$	18.6782	0.737745	0.368872	+	0.929480i	$0.379744\pi$
$642$	14.5245	0.573238
$643$	15.5969	0.615083	0.307541	−	0.951535i	$-0.400494\pi$
$643$	15.5969	0.615083	0.307541	+	0.951535i	$0.400494\pi$
$644$	−28.1371	−1.10876
$645$	0	0
$646$	8.91713	0.350840
$647$	26.3584	1.03626	0.518128	−	0.855303i	$-0.326629\pi$
$647$	26.3584	1.03626	0.518128	+	0.855303i	$0.326629\pi$
$648$	1.00000	0.0392837
$649$	−9.13798	−0.358697
$650$	0	0
$651$	−50.1948	−1.96729
$652$	−6.23874	−0.244328
$653$	19.6185	0.767731	0.383866	−	0.923389i	$-0.374593\pi$
$653$	19.6185	0.767731	0.383866	+	0.923389i	$0.374593\pi$
$654$	4.77065	0.186547
$655$	0	0
$656$	−1.73520	−0.0677483
$657$	7.22800	0.281991
$658$	41.9380	1.63491
$659$	23.1366	0.901273	0.450637	−	0.892707i	$-0.351197\pi$
$659$	23.1366	0.901273	0.450637	+	0.892707i	$0.351197\pi$
$660$	0	0
$661$	17.4970	0.680556	0.340278	−	0.940325i	$-0.389479\pi$
$661$	17.4970	0.680556	0.340278	+	0.940325i	$0.389479\pi$
$662$	−4.07299	−0.158301
$663$	−4.68363	−0.181897
$664$	−13.2741	−0.515134
$665$	0	0
$666$	−1.74607	−0.0676588
$667$	20.9452	0.811000
$668$	14.8368	0.574054
$669$	8.84212	0.341856
$670$	0	0
$671$	0.0761265	0.00293883
$672$	−4.80694	−0.185432
$673$	1.03454	0.0398785	0.0199393	−	0.999801i	$-0.493653\pi$
$673$	1.03454	0.0398785	0.0199393	+	0.999801i	$0.493653\pi$
$674$	−9.04782	−0.348509
$675$	0	0
$676$	−5.01824	−0.193009
$677$	−9.41420	−0.361817	−0.180909	−	0.983500i	$-0.557904\pi$
$677$	−9.41420	−0.361817	−0.180909	+	0.983500i	$0.557904\pi$
$678$	−4.83558	−0.185709
$679$	−87.8257	−3.37044
$680$	0	0
$681$	−17.6968	−0.678141
$682$	−9.21610	−0.352903
$683$	13.8607	0.530363	0.265182	−	0.964198i	$-0.414568\pi$
$683$	13.8607	0.530363	0.265182	+	0.964198i	$0.414568\pi$
$684$	5.37889	0.205667
$685$	0	0
$686$	−43.7753	−1.67135
$687$	−8.91363	−0.340076
$688$	2.27151	0.0866007
$689$	−10.0277	−0.382024
$690$	0	0
$691$	−9.10643	−0.346425	−0.173213	−	0.984884i	$-0.555415\pi$
$691$	−9.10643	−0.346425	−0.173213	+	0.984884i	$0.555415\pi$
$692$	−16.0369	−0.609630
$693$	4.24254	0.161161
$694$	8.68656	0.329737
$695$	0	0
$696$	3.57827	0.135634
$697$	−2.87662	−0.108960
$698$	26.8305	1.01555
$699$	−9.59063	−0.362751
$700$	0	0
$701$	−22.6848	−0.856791	−0.428396	−	0.903591i	$-0.640921\pi$
$701$	−22.6848	−0.856791	−0.428396	+	0.903591i	$0.640921\pi$
$702$	−2.82520	−0.106630
$703$	−9.39191	−0.354223
$704$	−0.882586	−0.0332637
$705$	0	0
$706$	−28.3499	−1.06696
$707$	26.2512	0.987278
$708$	10.3536	0.389114
$709$	22.4488	0.843084	0.421542	−	0.906809i	$-0.361489\pi$
$709$	22.4488	0.843084	0.421542	+	0.906809i	$0.361489\pi$
$710$	0	0
$711$	−12.5762	−0.471646
$712$	18.6866	0.700310
$713$	61.1225	2.28906
$714$	−7.96896	−0.298231
$715$	0	0
$716$	11.7489	0.439077
$717$	−9.16299	−0.342198
$718$	8.68830	0.324245
$719$	45.7054	1.70452	0.852262	−	0.523115i	$-0.175230\pi$
$719$	45.7054	1.70452	0.852262	+	0.523115i	$0.175230\pi$
$720$	0	0
$721$	31.9294	1.18911
$722$	9.93243	0.369647
$723$	−2.49551	−0.0928090
$724$	−4.03402	−0.149923
$725$	0	0
$726$	−10.2210	−0.379338
$727$	2.19423	0.0813793	0.0406897	−	0.999172i	$-0.487044\pi$
$727$	2.19423	0.0813793	0.0406897	+	0.999172i	$0.487044\pi$
$728$	13.5806	0.503330
$729$	1.00000	0.0370370
$730$	0	0
$731$	3.76572	0.139280
$732$	−0.0862540	−0.00318804
$733$	9.17807	0.339000	0.169500	−	0.985530i	$-0.445785\pi$
$733$	9.17807	0.339000	0.169500	+	0.985530i	$0.445785\pi$
$734$	−12.4713	−0.460325
$735$	0	0
$736$	5.85344	0.215761
$737$	−10.5562	−0.388842
$738$	−1.73520	−0.0638737
$739$	−43.5127	−1.60064	−0.800320	−	0.599572i	$-0.795337\pi$
$739$	−43.5127	−1.60064	−0.800320	+	0.599572i	$0.795337\pi$
$740$	0	0
$741$	−15.1964	−0.558255
$742$	−17.0616	−0.626350
$743$	−8.61668	−0.316115	−0.158058	−	0.987430i	$-0.550523\pi$
$743$	−8.61668	−0.316115	−0.158058	+	0.987430i	$0.550523\pi$
$744$	10.4422	0.382828
$745$	0	0
$746$	−12.9988	−0.475918
$747$	−13.2741	−0.485673
$748$	−1.46315	−0.0534982
$749$	−69.8186	−2.55112
$750$	0	0
$751$	1.11603	0.0407245	0.0203623	−	0.999793i	$-0.493518\pi$
$751$	1.11603	0.0407245	0.0203623	+	0.999793i	$0.493518\pi$
$752$	−8.72447	−0.318149
$753$	8.71262	0.317505
$754$	−10.1093	−0.368160
$755$	0	0
$756$	−4.80694	−0.174827
$757$	−37.2729	−1.35471	−0.677354	−	0.735658i	$-0.736873\pi$
$757$	−37.2729	−1.35471	−0.677354	+	0.735658i	$0.736873\pi$
$758$	1.75227	0.0636452
$759$	−5.16616	−0.187520
$760$	0	0
$761$	−20.0242	−0.725875	−0.362937	−	0.931814i	$-0.618226\pi$
$761$	−20.0242	−0.725875	−0.362937	+	0.931814i	$0.618226\pi$
$762$	−1.80181	−0.0652727
$763$	−22.9322	−0.830202
$764$	11.9215	0.431306
$765$	0	0
$766$	34.1359	1.23338
$767$	−29.2511	−1.05620
$768$	1.00000	0.0360844
$769$	−15.4698	−0.557855	−0.278927	−	0.960312i	$-0.589979\pi$
$769$	−15.4698	−0.557855	−0.278927	+	0.960312i	$0.589979\pi$
$770$	0	0
$771$	−19.7871	−0.712616
$772$	11.8088	0.425009
$773$	−24.0578	−0.865299	−0.432650	−	0.901562i	$-0.642421\pi$
$773$	−24.0578	−0.865299	−0.432650	+	0.901562i	$0.642421\pi$
$774$	2.27151	0.0816479
$775$	0	0
$776$	18.2706	0.655876
$777$	8.39326	0.301106
$778$	6.85652	0.245818
$779$	−9.33346	−0.334406
$780$	0	0
$781$	3.09574	0.110774
$782$	9.70385	0.347009
$783$	3.57827	0.127877
$784$	16.1067	0.575239
$785$	0	0
$786$	−16.0315	−0.571823
$787$	−33.3561	−1.18902	−0.594508	−	0.804089i	$-0.702653\pi$
$787$	−33.3561	−1.18902	−0.594508	+	0.804089i	$0.702653\pi$
$788$	−7.27842	−0.259283
$789$	25.5635	0.910083
$790$	0	0
$791$	23.2443	0.826473
$792$	−0.882586	−0.0313613
$793$	0.243685	0.00865350
$794$	−33.1587	−1.17676
$795$	0	0
$796$	2.27949	0.0807944
$797$	−32.6570	−1.15677	−0.578386	−	0.815763i	$-0.696317\pi$
$797$	−32.6570	−1.15677	−0.578386	+	0.815763i	$0.696317\pi$
$798$	−25.8560	−0.915292
$799$	−14.4634	−0.511680
$800$	0	0
$801$	18.6866	0.660259
$802$	3.51432	0.124095
$803$	−6.37933	−0.225122
$804$	11.9605	0.421816
$805$	0	0
$806$	−29.5012	−1.03914
$807$	24.4144	0.859428
$808$	−5.46110	−0.192121
$809$	10.3458	0.363740	0.181870	−	0.983323i	$-0.441785\pi$
$809$	10.3458	0.363740	0.181870	+	0.983323i	$0.441785\pi$
$810$	0	0
$811$	−38.0376	−1.33568	−0.667841	−	0.744304i	$-0.732781\pi$
$811$	−38.0376	−1.33568	−0.667841	+	0.744304i	$0.732781\pi$
$812$	−17.2005	−0.603620
$813$	2.74652	0.0963245
$814$	1.54106	0.0540140
$815$	0	0
$816$	1.65780	0.0580347
$817$	12.2182	0.427461
$818$	−16.2848	−0.569383
$819$	13.5806	0.474544
$820$	0	0
$821$	−20.0009	−0.698036	−0.349018	−	0.937116i	$-0.613485\pi$
$821$	−20.0009	−0.698036	−0.349018	+	0.937116i	$0.613485\pi$
$822$	−1.76718	−0.0616376
$823$	−39.2305	−1.36749	−0.683745	−	0.729721i	$-0.739650\pi$
$823$	−39.2305	−1.36749	−0.683745	+	0.729721i	$0.739650\pi$
$824$	−6.64235	−0.231397
$825$	0	0
$826$	−49.7694	−1.73170
$827$	54.9071	1.90931	0.954653	−	0.297720i	$-0.0962261\pi$
$827$	54.9071	1.90931	0.954653	+	0.297720i	$0.0962261\pi$
$828$	5.85344	0.203421
$829$	−6.52238	−0.226531	−0.113266	−	0.993565i	$-0.536131\pi$
$829$	−6.52238	−0.226531	−0.113266	+	0.993565i	$0.536131\pi$
$830$	0	0
$831$	2.98079	0.103402
$832$	−2.82520	−0.0979462
$833$	26.7017	0.925159
$834$	10.9965	0.380778
$835$	0	0
$836$	−4.74733	−0.164190
$837$	10.4422	0.360934
$838$	26.4881	0.915018
$839$	−43.4548	−1.50023	−0.750113	−	0.661309i	$-0.770001\pi$
$839$	−43.4548	−1.50023	−0.750113	+	0.661309i	$0.770001\pi$
$840$	0	0
$841$	−16.1960	−0.558483
$842$	−30.9522	−1.06668
$843$	3.86174	0.133006
$844$	−1.24920	−0.0429991
$845$	0	0
$846$	−8.72447	−0.299953
$847$	49.1319	1.68819
$848$	3.54936	0.121886
$849$	−16.7019	−0.573208
$850$	0	0
$851$	−10.2205	−0.350355
$852$	−3.50758	−0.120168
$853$	20.8621	0.714303	0.357152	−	0.934046i	$-0.383748\pi$
$853$	20.8621	0.714303	0.357152	+	0.934046i	$0.383748\pi$
$854$	0.414618	0.0141879
$855$	0	0
$856$	14.5245	0.496439
$857$	−10.2125	−0.348854	−0.174427	−	0.984670i	$-0.555807\pi$
$857$	−10.2125	−0.348854	−0.174427	+	0.984670i	$0.555807\pi$
$858$	2.49348	0.0851260
$859$	2.65350	0.0905362	0.0452681	−	0.998975i	$-0.485586\pi$
$859$	2.65350	0.0905362	0.0452681	+	0.998975i	$0.485586\pi$
$860$	0	0
$861$	8.34102	0.284261
$862$	−1.72282	−0.0586795
$863$	2.24175	0.0763099	0.0381549	−	0.999272i	$-0.487852\pi$
$863$	2.24175	0.0763099	0.0381549	+	0.999272i	$0.487852\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	24.1382	0.820248
$867$	−14.2517	−0.484013
$868$	−50.1948	−1.70372
$869$	11.0996	0.376529
$870$	0	0
$871$	−33.7909	−1.14496
$872$	4.77065	0.161555
$873$	18.2706	0.618366
$874$	31.4850	1.06500
$875$	0	0
$876$	7.22800	0.244211
$877$	−51.1183	−1.72614	−0.863071	−	0.505082i	$-0.831462\pi$
$877$	−51.1183	−1.72614	−0.863071	+	0.505082i	$0.831462\pi$
$878$	8.24333	0.278199
$879$	−0.503153	−0.0169709
$880$	0	0
$881$	−47.0341	−1.58462	−0.792309	−	0.610120i	$-0.791121\pi$
$881$	−47.0341	−1.58462	−0.792309	+	0.610120i	$0.791121\pi$
$882$	16.1067	0.542340
$883$	26.5897	0.894814	0.447407	−	0.894331i	$-0.352348\pi$
$883$	26.5897	0.894814	0.447407	+	0.894331i	$0.352348\pi$
$884$	−4.68363	−0.157527
$885$	0	0
$886$	22.4652	0.754733
$887$	−47.9343	−1.60948	−0.804739	−	0.593629i	$-0.797695\pi$
$887$	−47.9343	−1.60948	−0.804739	+	0.593629i	$0.797695\pi$
$888$	−1.74607	−0.0585943
$889$	8.66119	0.290487
$890$	0	0
$891$	−0.882586	−0.0295677
$892$	8.84212	0.296056
$893$	−46.9279	−1.57038
$894$	2.90948	0.0973076
$895$	0	0
$896$	−4.80694	−0.160589
$897$	−16.5371	−0.552159
$898$	30.4988	1.01776
$899$	37.3648	1.24619
$900$	0	0
$901$	5.88415	0.196029
$902$	1.53146	0.0509922
$903$	−10.9190	−0.363363
$904$	−4.83558	−0.160829
$905$	0	0
$906$	−1.34184	−0.0445796
$907$	5.35392	0.177774	0.0888870	−	0.996042i	$-0.471669\pi$
$907$	5.35392	0.177774	0.0888870	+	0.996042i	$0.471669\pi$
$908$	−17.6968	−0.587287
$909$	−5.46110	−0.181133
$910$	0	0
$911$	−13.5305	−0.448286	−0.224143	−	0.974556i	$-0.571958\pi$
$911$	−13.5305	−0.448286	−0.224143	+	0.974556i	$0.571958\pi$
$912$	5.37889	0.178113
$913$	11.7155	0.387727
$914$	−6.65272	−0.220053
$915$	0	0
$916$	−8.91363	−0.294515
$917$	77.0623	2.54482
$918$	1.65780	0.0547156
$919$	−55.7527	−1.83911	−0.919556	−	0.392958i	$-0.871452\pi$
$919$	−55.7527	−1.83911	−0.919556	+	0.392958i	$0.871452\pi$
$920$	0	0
$921$	−8.63375	−0.284492
$922$	−23.6681	−0.779469
$923$	9.90962	0.326179
$924$	4.24254	0.139569
$925$	0	0
$926$	26.0857	0.857229
$927$	−6.64235	−0.218163
$928$	3.57827	0.117462
$929$	−51.8168	−1.70006	−0.850028	−	0.526738i	$-0.823415\pi$
$929$	−51.8168	−1.70006	−0.850028	+	0.526738i	$0.823415\pi$
$930$	0	0
$931$	86.6360	2.83938
$932$	−9.59063	−0.314151
$933$	20.2674	0.663525
$934$	−1.47562	−0.0482839
$935$	0	0
$936$	−2.82520	−0.0923446
$937$	39.9648	1.30559	0.652797	−	0.757533i	$-0.273595\pi$
$937$	39.9648	1.30559	0.652797	+	0.757533i	$0.273595\pi$
$938$	−57.4936	−1.87723
$939$	−17.0302	−0.555760
$940$	0	0
$941$	−15.1125	−0.492652	−0.246326	−	0.969187i	$-0.579223\pi$
$941$	−15.1125	−0.492652	−0.246326	+	0.969187i	$0.579223\pi$
$942$	−8.31169	−0.270810
$943$	−10.1569	−0.330754
$944$	10.3536	0.336983
$945$	0	0
$946$	−2.00481	−0.0651818
$947$	34.0666	1.10702	0.553508	−	0.832844i	$-0.313289\pi$
$947$	34.0666	1.10702	0.553508	+	0.832844i	$0.313289\pi$
$948$	−12.5762	−0.408458
$949$	−20.4205	−0.662879
$950$	0	0
$951$	−2.82157	−0.0914956
$952$	−7.96896	−0.258275
$953$	−33.3709	−1.08099	−0.540494	−	0.841348i	$-0.681763\pi$
$953$	−33.3709	−1.08099	−0.540494	+	0.841348i	$0.681763\pi$
$954$	3.54936	0.114915
$955$	0	0
$956$	−9.16299	−0.296352
$957$	−3.15813	−0.102088
$958$	−13.4099	−0.433254
$959$	8.49475	0.274310
$960$	0	0
$961$	78.0387	2.51738
$962$	4.93300	0.159046
$963$	14.5245	0.468047
$964$	−2.49551	−0.0803749
$965$	0	0
$966$	−28.1371	−0.905297
$967$	26.4612	0.850936	0.425468	−	0.904974i	$-0.360110\pi$
$967$	26.4612	0.850936	0.425468	+	0.904974i	$0.360110\pi$
$968$	−10.2210	−0.328517
$969$	8.91713	0.286460
$970$	0	0
$971$	31.5954	1.01394	0.506972	−	0.861962i	$-0.330765\pi$
$971$	31.5954	1.01394	0.506972	+	0.861962i	$0.330765\pi$
$972$	1.00000	0.0320750
$973$	−52.8596	−1.69460
$974$	−2.12008	−0.0679318
$975$	0	0
$976$	−0.0862540	−0.00276092
$977$	−4.64054	−0.148464	−0.0742320	−	0.997241i	$-0.523651\pi$
$977$	−4.64054	−0.148464	−0.0742320	+	0.997241i	$0.523651\pi$
$978$	−6.23874	−0.199493
$979$	−16.4925	−0.527103
$980$	0	0
$981$	4.77065	0.152315
$982$	−2.22427	−0.0709793
$983$	33.9888	1.08408	0.542038	−	0.840354i	$-0.317653\pi$
$983$	33.9888	1.08408	0.542038	+	0.840354i	$0.317653\pi$
$984$	−1.73520	−0.0553162
$985$	0	0
$986$	5.93206	0.188915
$987$	41.9380	1.33490
$988$	−15.1964	−0.483463
$989$	13.2962	0.422794
$990$	0	0
$991$	−55.0594	−1.74902	−0.874509	−	0.485009i	$-0.838816\pi$
$991$	−55.0594	−1.74902	−0.874509	+	0.485009i	$0.838816\pi$
$992$	10.4422	0.331539
$993$	−4.07299	−0.129252
$994$	16.8607	0.534790
$995$	0	0
$996$	−13.2741	−0.420605
$997$	−0.730872	−0.0231470	−0.0115735	−	0.999933i	$-0.503684\pi$
$997$	−0.730872	−0.0231470	−0.0115735	+	0.999933i	$0.503684\pi$
$998$	14.5582	0.460832
$999$	−1.74607	−0.0552432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.v.1.1		8
5.2	odd	4		3750.2.c.k.1249.9		16
5.3	odd	4		3750.2.c.k.1249.8		16
5.4	even	2		3750.2.a.u.1.8		8
25.3	odd	20		150.2.h.b.109.2	✓	16
25.4	even	10		750.2.g.g.451.4		16
25.6	even	5		750.2.g.f.301.1		16
25.8	odd	20		750.2.h.d.199.4		16
25.17	odd	20		150.2.h.b.139.2	yes	16
25.19	even	10		750.2.g.g.301.4		16
25.21	even	5		750.2.g.f.451.1		16
25.22	odd	20		750.2.h.d.49.3		16
75.17	even	20		450.2.l.c.289.3		16
75.53	even	20		450.2.l.c.109.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.2	✓	16	25.3	odd	20
150.2.h.b.139.2	yes	16	25.17	odd	20
450.2.l.c.109.3		16	75.53	even	20
450.2.l.c.289.3		16	75.17	even	20
750.2.g.f.301.1		16	25.6	even	5
750.2.g.f.451.1		16	25.21	even	5
750.2.g.g.301.4		16	25.19	even	10
750.2.g.g.451.4		16	25.4	even	10
750.2.h.d.49.3		16	25.22	odd	20
750.2.h.d.199.4		16	25.8	odd	20
3750.2.a.u.1.8		8	5.4	even	2
3750.2.a.v.1.1		8	1.1	even	1	trivial
3750.2.c.k.1249.8		16	5.3	odd	4
3750.2.c.k.1249.9		16	5.2	odd	4

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.80694 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.80694 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.882586 q^{11} +1.00000 q^{12} -2.82520 q^{13} -4.80694 q^{14} +1.00000 q^{16} +1.65780 q^{17} +1.00000 q^{18} +5.37889 q^{19} -4.80694 q^{21} -0.882586 q^{22} +5.85344 q^{23} +1.00000 q^{24} -2.82520 q^{26} +1.00000 q^{27} -4.80694 q^{28} +3.57827 q^{29} +10.4422 q^{31} +1.00000 q^{32} -0.882586 q^{33} +1.65780 q^{34} +1.00000 q^{36} -1.74607 q^{37} +5.37889 q^{38} -2.82520 q^{39} -1.73520 q^{41} -4.80694 q^{42} +2.27151 q^{43} -0.882586 q^{44} +5.85344 q^{46} -8.72447 q^{47} +1.00000 q^{48} +16.1067 q^{49} +1.65780 q^{51} -2.82520 q^{52} +3.54936 q^{53} +1.00000 q^{54} -4.80694 q^{56} +5.37889 q^{57} +3.57827 q^{58} +10.3536 q^{59} -0.0862540 q^{61} +10.4422 q^{62} -4.80694 q^{63} +1.00000 q^{64} -0.882586 q^{66} +11.9605 q^{67} +1.65780 q^{68} +5.85344 q^{69} -3.50758 q^{71} +1.00000 q^{72} +7.22800 q^{73} -1.74607 q^{74} +5.37889 q^{76} +4.24254 q^{77} -2.82520 q^{78} -12.5762 q^{79} +1.00000 q^{81} -1.73520 q^{82} -13.2741 q^{83} -4.80694 q^{84} +2.27151 q^{86} +3.57827 q^{87} -0.882586 q^{88} +18.6866 q^{89} +13.5806 q^{91} +5.85344 q^{92} +10.4422 q^{93} -8.72447 q^{94} +1.00000 q^{96} +18.2706 q^{97} +16.1067 q^{98} -0.882586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{13} + 4 q^{14} + 8 q^{16} + 14 q^{17} + 8 q^{18} + 10 q^{19} + 4 q^{21} + 6 q^{22} + 12 q^{23} + 8 q^{24} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 10 q^{29} + 16 q^{31} + 8 q^{32} + 6 q^{33} + 14 q^{34} + 8 q^{36} - 6 q^{37} + 10 q^{38} + 2 q^{39} + 6 q^{41} + 4 q^{42} + 2 q^{43} + 6 q^{44} + 12 q^{46} + 14 q^{47} + 8 q^{48} + 26 q^{49} + 14 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{54} + 4 q^{56} + 10 q^{57} + 10 q^{58} + 16 q^{61} + 16 q^{62} + 4 q^{63} + 8 q^{64} + 6 q^{66} - 6 q^{67} + 14 q^{68} + 12 q^{69} + 6 q^{71} + 8 q^{72} - 8 q^{73} - 6 q^{74} + 10 q^{76} + 8 q^{77} + 2 q^{78} + 10 q^{79} + 8 q^{81} + 6 q^{82} + 22 q^{83} + 4 q^{84} + 2 q^{86} + 10 q^{87} + 6 q^{88} + 20 q^{89} + 6 q^{91} + 12 q^{92} + 16 q^{93} + 14 q^{94} + 8 q^{96} - 16 q^{97} + 26 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^13 + 4 * q^14 + 8 * q^16 + 14 * q^17 + 8 * q^18 + 10 * q^19 + 4 * q^21 + 6 * q^22 + 12 * q^23 + 8 * q^24 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 10 * q^29 + 16 * q^31 + 8 * q^32 + 6 * q^33 + 14 * q^34 + 8 * q^36 - 6 * q^37 + 10 * q^38 + 2 * q^39 + 6 * q^41 + 4 * q^42 + 2 * q^43 + 6 * q^44 + 12 * q^46 + 14 * q^47 + 8 * q^48 + 26 * q^49 + 14 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^54 + 4 * q^56 + 10 * q^57 + 10 * q^58 + 16 * q^61 + 16 * q^62 + 4 * q^63 + 8 * q^64 + 6 * q^66 - 6 * q^67 + 14 * q^68 + 12 * q^69 + 6 * q^71 + 8 * q^72 - 8 * q^73 - 6 * q^74 + 10 * q^76 + 8 * q^77 + 2 * q^78 + 10 * q^79 + 8 * q^81 + 6 * q^82 + 22 * q^83 + 4 * q^84 + 2 * q^86 + 10 * q^87 + 6 * q^88 + 20 * q^89 + 6 * q^91 + 12 * q^92 + 16 * q^93 + 14 * q^94 + 8 * q^96 - 16 * q^97 + 26 * q^98 + 6 * q^99

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